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Elementary Mathematics

Assessment Handbook

September 2015

edTPA stems from a twenty-five-year history of developing performance-based assessments

of teaching quality and effectiveness. The Teacher Performance Assessment Consortium

(Stanford and AACTE) acknowledges the National Board for Professional Teaching

Standards, the Interstate Teacher Assessment and Support Consortium, and the

Performance Assessment for California Teachers for their pioneering work using discipline-

specific portfolio assessments to evaluate teaching quality. This version of the handbook has

been developed with thoughtful input from over six hundred teachers and teacher educators

representing various national design teams, national subject matter organizations (ACEI,

ACTFL, AMLE, CEC, IRA, NAEYC, NAGC, NCSS, NCTE, NCTM, NSTA, SHAPE America),

and content validation reviewers. All contributions are recognized and appreciated.

This document was authored by the Stanford Center for Assessment, Learning and Equity (SCALE)

with editorial and design assistance from Evaluation Systems.

The edTPA trademarks are owned by The Board of Trustees of the Leland Stanford Junior University. Use of the

edTPA trademarks is permitted only pursuant to the terms of a written license agreement.

edTPA Elementary Mathematics Assessment Handbook

Contents

Introduction to edTPA Elementary Mathematics .................................................................... 1

Purpose................................................................................................................................................................... 1

Overview of the Assessment ................................................................................................................................... 1

Structure of the Handbook ...................................................................................................................................... 4

edTPA Elementary Mathematics Tasks Overview .................................................................................................. 6

Planning Task 1: Planning for Instruction and Assessment .................................................. 9

What Do I Need to Think About? ............................................................................................................................ 9

What Do I Need to Do? ........................................................................................................................................... 9

What Do I Need to Write? ..................................................................................................................................... 11

How Will the Evidence of My Teaching Practice Be Assessed? ........................................................................... 14

Planning Rubrics ................................................................................................................................................... 15

Instruction Task 2: Instructing and Engaging Students in Learning ................................... 20

What Do I Need to Think About? .......................................................................................................................... 20

What Do I Need to Do? ......................................................................................................................................... 20

What Do I Need to Write? ..................................................................................................................................... 21

How Will the Evidence of My Teaching Practice Be Assessed? ........................................................................... 22

Instruction Rubrics ................................................................................................................................................ 23

Assessment Task 3: Assessing Student Learning ............................................................... 28

What Do I Need to Think About? .......................................................................................................................... 28

What Do I Need to Do? ......................................................................................................................................... 28

What Do I Need to Write? ..................................................................................................................................... 29

How Will the Evidence of My Teaching Practice Be Assessed? ........................................................................... 31

Assessment Rubrics ............................................................................................................................................. 32

Professional Responsibilities ................................................................................................ 37

Elementary Mathematics Context for Learning Information ................................................ 38

Elementary Mathematics Evidence Chart ............................................................................. 41

Planning Task 1: Artifacts and Commentary Specifications .................................................................................. 41

Instruction Task 2: Artifacts and Commentary Specifications ............................................................................... 42

Assessment Task 3: Artifacts and Commentary Specifications ............................................................................ 43

Elementary Mathematics Glossary ........................................................................................ 46

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Introduction to edTPA Elementary

Mathematics

Purpose

The purpose of edTPA Elementary Mathematics, a nationally available performance-based

assessment, is to measure novice teachers’ readiness to teach elementary mathematics. The

assessment is designed with a focus on student learning and principles from research and

theory. It is based on findings that successful teachers

 develop knowledge of subject matter, content standards, and subject-specific

pedagogy

 develop and apply knowledge of varied students’ needs

 consider research and theory about how students learn

 reflect on and analyze evidence of the effects of instruction on student learning

As a performance-based assessment, edTPA is designed to engage candidates in

demonstrating their understanding of teaching and student learning in authentic ways.

Overview of the Assessment

The edTPA Elementary Mathematics assessment is composed of three tasks:

1. Planning for Instruction and Assessment

2. Instructing and Engaging Students in Learning

3. Assessing Student Learning

For this assessment, you will first plan 3–5 consecutive mathematics lessons (or, if

teaching within a large time block, 3–5 hours of connected instruction) referred to as a

learning segment. Consistent with the Principles and Standards for School Mathematics

(NCTM 2000), a learning segment prepared for this assessment should reflect a balanced

approach to mathematics. This means your segment should include learning tasks where

students have opportunities to develop

 conceptual understanding

 procedural fluency

 mathematical reasoning and/or problem-solving skills

 precise communication skills

You will then teach the learning segment, making a videorecording of your interactions with

students during instruction. You will also assess, informally and formally, students’ learning

throughout the learning segment. Upon completion of the three tasks, you will submit

artifacts from the tasks (e.g., lesson plans, clips from your videorecording, assessment

materials, instructional materials, student work samples), as well as commentaries that you

have written to explain and reflect on the Planning, Instruction, and Assessment

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components of the tasks. The artifacts and commentaries for each task will then be

evaluated using rubrics especially developed for each task.

You will complete three tasks for edTPA:

1. Planning for Instruction and Assessment

2. Instructing and Engaging Students in Learning

3. Assessing Student Learning

The edTPA Tasks and the Cycle of Effective Teaching

The three edTPA tasks represent a cycle of effective teaching (i.e., teaching that is focused on

student learning). Planning Task 1 documents your intended teaching, Instruction Task 2

documents your enacted teaching, and Assessment Task 3 documents the impact of your

teaching on student learning.

The three tasks and the evidence you provide for each are framed by your understandings of

your students and their learning. As you develop, document, and teach your lessons, you will

reflect upon the cyclical relationship among planning, instruction, and assessment with a focus

on your students’ learning needs.

Evidence of Teaching Practice: Artifacts and Commentaries

An essential part of edTPA is the evidence you will submit of how you planned, taught, and

assessed your lessons to deepen student learning in mathematics. This evidence includes

both artifacts and commentaries:

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 Artifacts represent authentic work completed by you and your students. These

include lesson plans, copies of instructional and assessment materials, video clips of

your teaching, and student work samples.

 Commentaries are your opportunity to describe your artifacts, explain the rationale

behind their choice, and analyze what you have learned about your teaching practice

and your students’ learning. Note that although your writing ability will not be scored

directly, commentaries must be clearly written and well-focused.

When preparing your artifacts and commentaries, refer to the rubrics frequently to guide

your thinking, planning, and writing. Refer to the Elementary Mathematics Evidence Chart

for information about how your evidence should be formatted for electronic submission.

Evaluation Criteria

The evidence (i.e., artifacts and commentaries) you submit will be judged on five

components of teaching practice:

1. Planning

2. Instruction

3. Assessment

4. Analyzing Teaching

5. Academic Language

You will provide evidence for the Planning, Instruction, and Assessment components within

the corresponding tasks. You will provide evidence for the Analyzing Teaching component

across all three tasks. You will provide evidence for the Academic Language component in

Planning Task 1, as well as in Instruction Task 2 AND/OR Assessment Task 3.

The rubrics used to score your performance on the edTPA portfolio are included in this

handbook, following the sections describing the directions for each task. The descriptors in

the five-level rubrics address a wide range of performance, beginning with the knowledge

and skills of a novice not ready to teach (Level 1) and extending to the advanced practices

of a highly accomplished beginner (Level 5).

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Structure of the Handbook

The following pages provide specific instructions on how to complete each of the three tasks

of the edTPA Elementary Mathematics assessment. After an overview of the tasks, the

handbook provides instructions for each task, organized into four sections:

1. What Do I Need to Think About?

This section provides focus questions for you to think about when completing the

task.

2. What Do I Need to Do?

This section provides specific, detailed directions for completing the task.

3. What Do I Need to Write?

This section tells you what you need to write and also provides specific and detailed

directions for writing the

commentary for the task.

4. How Will the Evidence of My Teaching Practice Be Assessed?

This section includes the rubrics that will be used to assess the evidence you provide for

the task.

Additional requirements and resources are provided for you in this handbook:

 Professional Responsibilities: guidelines for the development of your evidence

 Elementary Mathematics Context for Learning Information: prompts used to

collect information about your school/classroom context

 Elementary Mathematics Evidence Chart: specifications for electronic submission

of evidence (artifacts and commentaries), including templates, supported file types,

number of files, response length, and other important evidence specifications

 Glossary: definitions of key terms can be accessed by rolling your cursor over each

glossary term marked with a dotted underline throughout the handbook or by

referring to the Elementary Mathematics Glossary

You should review the Making Good Choices document prior to beginning the planning of

the learning segment. If you are in a preparation program, it will have additional resources

that provide guidance as you develop your evidence.

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Review all instructions carefully before beginning to teach the learning segment to

ensure that you are well prepared for all tasks. Before you record your videos,

pay particular attention to the specific content focus of each video clip

submission; these foci are described in the What Do I Need to Do? sections in

Instruction Task 2 and Assessment Task 3. Refer to the Professional

Responsibilities section of this handbook for important information about

permissions, confidentiality, and other requirements.

If your program requires you to submit artifacts and commentaries for official

scoring, refer to www.edTPA.com for complete and current information before

beginning your work and to download templates for submitting materials. The

website contains information about the registration process, submission deadlines,

submission requirements, withdrawal/refund policies, and score reporting. It also

provides contact information should you have questions about your registration and

participation in edTPA.

Whether submitting directly to www.edTPA.com or via your program’s electronic

portfolio management system, follow the submission guidelines as documented in

the Evidence Chart and review edTPA Submission Requirements to ensure that

your materials conform to the required evidence specifications and requirements for

scoring.

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edTPA Elementary Mathematics Tasks Overview

Planning Task 1: Planning for Instruction and Assessment

What to Do

►

Select one class as a focus for this

assessment.

►

Provide relevant context information.

►

Identify a learning segment to plan,

teach, and analyze student learning.

Your learning segment should include

3–5 consecutive lessons (or, if

teaching mathematics within a large

time block, about 3–5 hours of

connected instruction).

►

Determine a central focus for your

learning segment. The central focus

should support students to develop

conceptual understanding, procedural

fluency, and mathematical reasoning

and/or problem-solving skills.

►

Write and submit a lesson plan for

each lesson in the learning segment.

►

Select and submit key instructional

materials needed to understand what

you and the students will be doing.

►

Choose one language function and

other language demands important to

understanding elementary

mathematics in your learning segment.

Identify a learning task where students

are supported to use this language.

►

Respond to commentary prompts prior

to teaching the learning segment.

►

Submit copies of all written

assessments and/or clear directions for

any oral or performance assessments

from the learning segment.



What to Submit

Part A: Context for

Learning Information

Part B: Lesson Plans for

Learning Segment

Part C: Instructional

Materials

Part D: Assessments

Part E: Planning

Commentary



Evaluation Rubrics

Planning Rubrics

Rubric 1: Planning for

Mathematical Understandings

Rubric 2: Planning to Support

Varied Student Learning Needs

Rubric 3: Using Knowledge of

Students to Inform Teaching and

Learning

Rubric 4: Identifying and

Supporting Language Demands

Rubric 5: Planning Assessments

to Monitor and Support Student

Learning

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Instruction Task 2: Instructing and Engaging Students in Learning

What to Do

►

Obtain required permissions for

videorecording from parents/guardians

of your students and other adults

appearing in the video.

►

Identify lessons from the learning

segment you planned in Planning Task

1 to be videorecorded. You should

choose lessons that show you

interacting with students to develop

their understanding of mathematics

concepts.

►

Videorecord your teaching and select

1 or 2 video clip(s) (no more than 15

minutes total).

►

Analyze your teaching and your

students’ learning in the video clip(s)

by responding to commentary prompts.

What to Submit

 Part A: Video Clips

 Part B: Instruction

Commentary

Evaluation Rubrics

Instruction Rubrics

Rubric 6: Learning Environment

Rubric 7: Engaging Students in

Learning

Rubric 8: Deepening Student

Learning

Rubric 9: Subject-Specific

Pedagogy: Using

Representations

Rubric 10: Analyzing Teaching

Effectiveness

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Assessment Task 3: Assessing Student Learning

What to Do

►

Select one assessment from the

learning segment that you will use to

evaluate your students’ developing

knowledge and skills. Attach the

assessment used to evaluate student

performance to the end of the

Assessment Commentary.

►

Define and submit the evaluation

criteria you will use to analyze student

learning.

►

Collect and analyze student work from

the selected assessment to identify

quantitative and qualitative patterns

of learning within and across learners

in the class.

►

Select 3 student work samples to

illustrate your analysis of patterns of

learning within and across learners in

the class. At least 1 of the samples

must be from a student with specific

learning needs. These 3 students will

be your focus students.

►

Summarize the learning of the whole

class, referring to work samples from

the 3 focus students to illustrate

patterns in student understanding

across the class.

►

Submit feedback for the work samples

for the 3 focus students in written,

audio, or video form.

►

Analyze evidence of students’

language use from (1) the video clips

from Instruction Task 2, (2) an

additional video clip of one or more

students using language within the

learning segment, AND/OR (3) the

student work samples from

Assessment Task 3.

►

Analyze evidence of student learning

and plan for next steps by responding

to commentary prompts.

What to Submit

 Part A: Student Work

Samples

 Part B: Evidence of

Feedback

 Part C: Assessment

Commentary

 Part D: Evaluation Criteria

Evaluation Rubrics

Assessment Rubrics

Rubric 11: Analysis of Student

Learning

Rubric 12: Providing Feedback

to Guide Learning

Rubric 13: Student Use of

Feedback

Rubric 14: Analyzing Students’

Language Use and Mathematics

Learning

Rubric 15: Using Assessment to

Inform Instruction

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Planning Task 1: Planning for Instruction

and Assessment

What Do I Need to Think About?

In Planning Task 1, you will describe your plans for the learning segment and explain how

your instruction is appropriate for the students and the content you are teaching. As you

develop your plans, you need to think about the following:

 What do your students know, what can they do, and what are they learning to do?

 What do you want your students to learn? What are the important understandings

and core concepts you want students to develop within the learning segment?

 How will you use your knowledge of your students’ assets to inform your plans?

 What instructional strategies, learning tasks, and assessments will you design to

support student learning and language use?

 How will your learning segment support students to develop and use language that

deepens content understanding?

 How is the teaching you propose supported by research and theory about how

students learn?

What Do I Need to Do?

 Select a class. If you teach more than one class, select one focus class for this

assessment. If your placement for mathematics has you responsible for a group rather

than a whole class, plans should describe instruction for that group (minimum of 4

students). That group will constitute “the whole class” for edTPA.

 Provide context information. The Elementary Mathematics Context for Learning

Information form is provided later in this handbook and must be submitted in a template.

This form provides essential information about your students and your school/classroom.

The context information you submit should be no more than 4 pages, including the

prompts.

 Identify a learning segment to plan, teach, and analyze. Review the curriculum with

your cooperating teacher and select a learning segment of 3–5 consecutive lessons. (If

teaching mathematics within a large time block, select a learning segment of about 3–5

hours of connected instruction.)

 Identify a central focus. Identify the central focus along with the content standards and

objectives you will address in the learning segment. The central focus should support

students in developing

 conceptual understanding

 procedural fluency

 mathematical reasoning and/or problem-solving skills

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 Identify and plan to support language demands. Select a key language function from

your learning objectives. Choose a learning task that provides opportunities for students

to practice using that language function. Identify additional language demands

associated with that task. Plan targeted supports that address the identified language

demands, including the language function.

 Write a lesson plan for each lesson in the learning segment. Your lesson plans should

be detailed enough that a substitute or other teacher could understand them well enough

to use them.

 Your lesson plans must include the following information, even if your teacher

preparation program requires you to use a specific lesson plan format:

 State-adopted student academic content standards that are the target of student

learning. (Note: Please include the number and text of each standard that is being

addressed. If only a portion of a standard is being addressed, then only list the part

or parts that are relevant.)

 Learning objectives associated with the content standards

 Informal and formal assessments used to monitor student learning, including type(s)

of assessment and what is being assessed

 Instructional strategies and learning tasks (including what you and the students will

be doing) that support diverse student needs

 Instructional resources and materials used to engage students in learning

 Each lesson plan must be no more than 4 pages in length. You will need to

condense or excerpt lesson plans longer than 4 pages. Any explanations or rationale for

decisions should be included in your Planning Commentary and deleted from your plans.

 Respond to the commentary prompts listed in the Planning Commentary section

prior to teaching the learning segment.

 Submit your original lesson plans. If you make changes while teaching the learning

segment, you may offer reflection on those changes in the Instruction Task 2 and

Assessment Task 3 Commentaries.

 Select and submit key instructional materials needed to understand what you and

the students will be doing (no more than 5 additional pages per lesson plan). The

instructional materials might include such items as class handouts, assignments, slides,

and interactive whiteboard images.

 Submit copies of all written assessments and/or directions for any oral or

performance assessments

. (Submit only the blank assessment given to students; do

not submit student work samples for this task.)

 Provide citations for the source of all materials that you did not create (e.g.,

published texts, websites, and material from other educators). List all citations by lesson

number at the end of the Planning Commentary.

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See the Planning Task 1: Artifacts and Commentary Specifications in the

Elementary Mathematics Evidence Chart for instructions on electronic submission of

evidence. This evidence chart identifies templates, supported file types, number of

files, response length, and other important evidence specifications. Your evidence

cannot contain hyperlinked content. Any web content you wish to include as part of

your evidence must be submitted as a document file, which must conform to the file

format and response length requirements.

What Do I Need to Write?

In Planning Task 1, you will write

 a description of your context for learning (see “What Do I Need to Do?” above for

directions)

 lesson plans (see “What Do I Need to Do?” above for directions)

 a commentary explaining your plans (see “Planning Commentary” below for

directions)

Planning Commentary

In Planning Task 1, you will write a commentary, responding to the prompts below. Your

commentary should be no more than 9 single-spaced pages, including the prompts.

1. Central Focus

a. Describe the central focus and purpose of the content you will teach in the learning

segment.

b. Given the central focus, describe how the standards and learning objectives within

your learning segment address

 conceptual understanding

 procedural fluency AND

 mathematical reasoning or problem-solving skills

c. Explain how your plans build on each other to help students make connections

between

 concepts

 computations/procedures AND

 mathematical reasoning or problem-solving strategies

to build understanding of mathematics.

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2. Knowledge of Students to Inform Teaching

For each of the prompts below (2a–c), describe what you know about your students

with respect to the central focus of the learning segment.

Consider the variety of learners in your class who may require different

strategies/support (e.g., students with IEPs or 504 plans, English language learners,

struggling readers, underperforming students or those with gaps in academic

knowledge, and/or gifted students).

a. Prior academic learning and prerequisite skills related to the central focus—Cite

evidence of what students know, what they can do, and what they are learning

to do.

b. Personal, cultural, and community assets related to the central focus—What do you

know about your students’ everyday experiences, cultural and language

backgrounds and practices, and interests?

c. Mathematical dispositions related to the central focus—What do you know about

the extent to which your students

 perceive mathematics as “sensible, useful, and worthwhile”

 persist in applying mathematics to solve problems

 believe in their own ability to learn mathematics

3. Supporting Students’ Mathematics Learning

Respond to prompts below (3a–c). To support your justifications, refer to the

instructional materials and lesson plans you have included as part of Planning

Task 1. In addition, use principles from research and/or theory to support your

justifications.

a. Justify how your understanding of your students’ prior academic learning; personal,

cultural, and community assets; and mathematical dispositions (from prompts 2a–c

above) guided your choice or adaptation of learning tasks and materials. Be explicit

about the connections between the learning tasks and students’ prior academic

learning, their assets, their mathematical dispositions, and research/theory.

b. Describe and justify why your instructional strategies and planned supports are

appropriate for the whole class, individuals, and/or groups of students with

specific learning needs.

Consider the variety of learners in your class who may require different

strategies/support (e.g., students with IEPs or 504 plans, English language

learners, struggling readers, underperforming students or those with gaps in

academic knowledge, and/or gifted students).

c. Describe common mathematical preconceptions, errors, or misunderstandings within

your central focus and how you will address them.

From the Common Core State Standards for Mathematics

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4. Supporting Mathematics Development Through Language

As you respond to prompts 4a–d, consider the range of students’ language assets

and needs—what do students already know, what are they struggling with, and/or

what is new to them?

a. Language Function. Using information about your students’ language assets

and needs, identify one language function essential for students to develop

conceptual understanding, procedural fluency, mathematical reasoning, or

problem-solving skills within your central focus. Listed below are some sample

language functions. You may choose one of these or another language function

more appropriate for your learning segment:

Categorize Compare/contrast Describe Interpret Justify

Please see additional examples and non-examples of language functions in the

glossary.

b. Identify a key learning task from your plans that provides students with opportunities

to practice using the language function identified above. Identify the lesson in which

the learning task occurs. (Give lesson day/number.)

c. Additional Language Demands. Given the language function and learning task

identified above, describe the following associated language demands (written or

oral) students need to understand and/or use:

 Vocabulary and/or symbols

 Plus at least one of the following:

 Syntax

 Discourse

d. Language Supports. Refer to your lesson plans and instructional materials as

needed in your response to the prompt.

 Identify and describe the planned instructional supports (during and/or prior to

the learning task) to help students understand, develop, and use the

identified language demands (vocabulary and/or symbols, function,

discourse, syntax).

5. Monitoring Student Learning

In response to the prompts below, refer to the assessments you will submit as part of

the materials for Planning Task 1.

a. Describe how your planned formal and informal assessments will provide direct

evidence of students’ conceptual understanding, computational/procedural fluency,

AND mathematical reasoning or problem-solving skills throughout the learning

segment.

b. Explain how the design or adaptation of your planned assessments allows students

with specific needs to demonstrate their learning.

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Consider the variety of learners in your class who may require different

strategies/support (e.g., students with IEPs or 504 plans, English language learners,

struggling readers, underperforming students or those with gaps in academic

knowledge, and/or gifted students).

How Will the Evidence of My Teaching Practice Be

Assessed?

For Planning Task 1, your evidence will be assessed using rubrics 1–5, which appear in the

following pages. When preparing your artifacts and commentaries, refer to the rubrics

frequently to guide your thinking, planning, and writing.

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Planning Rubrics

Rubric 1: Planning for Mathematical Understandings

How do the candidate’s plans build students’ conceptual understanding, procedural fluency, AND mathematical

reasoning or problem-solving skills?

Level 1

Candidate’s plans for

instruction focus solely on

facts and/or procedures with

no connections to

• concepts OR

• mathematical reasoning or

problem-solving skills.

There are significant content

inaccuracies that will lead to

student misunderstandings.

Standards, objectives, and

learning tasks and materials

are not aligned with each

other.

Level 2

Candidate’s plans for

instruction support student

learning of facts and

procedures with vague

connections to

• concepts OR

• mathematical reasoning or

problem-solving skills.

Level 3

Candidate’s plans for

instruction build on each

other to support learning of

facts and procedures with

clear connections to

• concepts OR

• mathematical reasoning or

problem-solving skills.

Level 4

Candidate’s plans for

instruction build on each other

to support learning of facts and

procedures with clear and

consistent connections to

• concepts AND

• mathematical reasoning or

problem-solving skills.

Level 5

Level 4 plus:

Candidate explains how they

will use learning tasks and

materials to lead students to

make clear and consistent

connections.

Text representing key differences between adjacent score levels is shown in bold. Evidence that does not meet Level 1 criteria is scored at Level 1.

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Planning Rubrics continued

Rubric 2: Planning to Support Varied Student Learning Needs

How does the candidate use knowledge of his/her students to target support for students to develop conceptual

understanding, procedural fluency, AND mathematical reasoning or problem-solving skills?

Level 1

There is no evidence of

planned supports.

Candidate does NOT attend

to ANY INSTRUCTIONAL

requirements in IEPs and

504 plans.

Level 2

Planned supports are loosely

tied to learning objectives or

the central focus of the

learning segment.

Level 3

Planned supports are tied to

learning objectives and the

central focus with attention to

the characteristics of the

class as a whole.

Level 4

Planned supports are tied to

learning objectives and the

central focus. Supports

address the needs of

specific individuals or

groups with similar needs.

Level 5

Level 4 plus:

Supports include specific

strategies to identify and

respond to preconceptions,

common errors, and

misunderstandings.

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Planning Rubrics continued

Rubric 3: Using Knowledge of Students to Inform Teaching and Learning

How does the candidate use knowledge of his/her students to justify instructional plans?

Level 1

Candidate’s justification of

learning tasks is either

missing OR represents a

deficit view of students and

their backgrounds.

Level 2

Candidate justifies learning

tasks with limited attention to

students’

• prior academic learning

• personal, cultural, or

community assets.

Level 3

Candidate justifies why

learning tasks (or their

adaptations) are appropriate

using examples of students’

• prior academic learning OR

• personal, cultural, or

community assets.

Candidate makes superficial

connections to research

and/or theory.

Level 4

Candidate justifies why

learning tasks (or their

adaptations) are appropriate

using examples of students’

• prior academic learning

AND

• personal, cultural, or

community assets.

Candidate makes

connections to research

and/or theory.

Level 5

Level 4 plus:

Candidate’s justification is

supported by principles from

research and/or theory.

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Planning Rubrics continued

Rubric 4: Identifying and Supporting Language Demands

How does the candidate identify and support language demands associated with a key mathematics learning

task?

Level 1

Language demands

identified by the candidate are

not consistent with the

selected language function

OR task.

Language supports are

missing or are not aligned

with the language demand(s)

for the learning task.

Level 2

Language supports primarily

address one language

demand (vocabulary and/or

symbols, function, discourse,

syntax).

Level 3

General language supports

address use of two or more

language demands

(vocabulary and/or symbols,

function, discourse, syntax).

Level 4

Targeted language supports

address use of

• vocabulary and/or symbols,

• language function, AND

• one or more additional

language demands

(discourse, syntax).

Level 5

Level 4 plus:

Language supports are

designed to meet the needs

of students with different

levels of language learning.

Language demands include: language function, vocabulary and/or symbols, syntax, and discourse (organizational structures, text structure, etc.).

Language function refers to the learning outcome (verb) selected in Planning Commentary Prompt 4a (e.g., categorize, describe).

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Planning Rubrics continued

Rubric 5: Planning Assessments to Monitor and Support Student Learning

How are the informal and formal assessments selected or designed to monitor students’ conceptual

understanding, procedural fluency, AND mathematical reasoning/problem-solving skills?

Level 1

The assessments only

provide evidence of students'

procedural skills or factual

knowledge.

Candidate does not attend to

ANY ASSESSMENT

requirements in IEPs and

504 plans.

Level 2

The assessments provide

limited evidence to monitor

students’

• conceptual understanding,

• procedural fluency, OR

• mathematical reasoning or

problem-solving skills

during the learning segment.

Level 3

The assessments provide

evidence to monitor students’

• conceptual understanding,

• procedural fluency, AND

• mathematical reasoning or

problem-solving skills

during the learning segment.

Level 4

The assessments provide

multiple forms of evidence to

monitor students’ progress

toward developing

• conceptual understanding,

• procedural fluency, AND

• mathematical reasoning or

problem-solving skills

throughout the learning

segment.

Level 5

Level 4 plus:

The assessments are

strategically designed to

allow individuals or groups

with specific needs to

demonstrate their learning.

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Instruction Task 2: Instructing and

Engaging Students in Learning

What Do I Need to Think About?

In Instruction Task 2, you will demonstrate how you support and engage students in

learning. Before you begin your instruction, you need to think about the following:

 What kind of learning environment do you want to develop in order to establish

respect and rapport, and to support students’ engagement in learning?

 What kinds of learning tasks actively engage students in the central focus of the

learning segment?

 How will you elicit and build on student responses in ways that develop and deepen

content understanding?

 In what ways will you connect new content to your students’ prior academic learning

and personal, cultural, or community assets during your instruction?

 How will you use evidence from your instruction to examine and change your

teaching practices to more effectively meet a variety of student learning needs?

What Do I Need to Do?

 Obtain required permission for videorecording. Before you record your video, ensure

that you have the appropriate permission from the parents/guardians of your students

and from adults who appear in the video. Adjust the camera angle to exclude individuals

for whom you do not have permission to film.

 Examine your lesson plans for the learning segment and identify challenging

learning tasks in which you and your students are actively engaged. The video clip(s)

you select for submission should provide a sample of how you interact with students to

develop understanding of mathematical concepts.

 Identify lessons to videorecord.

 Provide 1–2 video clip(s) (together totaling no more than 15 minutes) that demonstrate

how you engage students in developing understandings of mathematical concepts.

 (Optional) Provide evidence of students’ language use. You may provide evidence

of language use with your video clip(s) from Instruction Task 2, an additional video clip of

one or more students using language within the learning segment (no more than 5

minutes in length), AND/OR through the student work samples analyzed in

Assessment Task 3.

 Determine whether you will feature the whole class or a targeted group of students

(minimum of 4 students) within the class.

 Videorecord your classroom teaching. Tips for videorecording your class are

available from your teacher preparation program.

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 Select video clip(s) to submit and verify that the clip(s) meet the following

requirements:



Check the video and sound quality to ensure that you and your students can be seen

and heard on the video clip(s) you submit. If most of the audio in a clip cannot be

understood by a scorer, submit another clip. If there are occasional audio portions

of a clip that cannot be understood that are relevant to your commentary responses,

do one of the following: 1) provide a transcript with time stamps of the inaudible

portion and refer to the transcript in your response; 2) embed quotes with time-stamp

references in the commentary response; or 3) insert captions in the video (captions

for this purpose will be considered permissible editing).

 A video clip must be continuous and unedited, with no interruption in events.

 If you have inadvertently included individuals for whom you do not have permission

to film in the video clip(s) you plan to submit, you may use software to blur the faces

of these individuals. This is not considered editing. Other portions of the submitted

video clip(s), including the classroom, your face, and the faces of individuals for

whom you have obtained permission to film, should remain unblurred.

 Do not include the name of the state, school, or district in your video. Use first names

only for all individuals appearing in the video.

 Respond to the prompts listed in the Instruction Commentary section below after

viewing the video clip(s).

 Determine if additional information is needed to understand what you and the

students are doing in the video clip(s). For example, if there are graphics, texts, or

images that are not clearly visible in the video, or comments that are not clearly heard,

you may insert digital copies or transcriptions at the end of the Instruction Commentary

(no more than 2 pages in addition to the responses to commentary prompts).

See the Instruction Task 2: Artifacts and Commentary Specifications in the

Elementary Mathematics Evidence Chart for instructions on electronic submission of

evidence. This chart identifies templates, supported file types, number of files,

response length, and other important evidence specifications. Your evidence cannot

contain hyperlinked content. Any web content you wish to include as part of your

evidence must be submitted as a document file, which must conform to the file

format and response length requirements.

What Do I Need to Write?

Instruction Commentary

In Instruction Task 2, you will write a commentary responding to the prompts below. Your

commentary should be no more than 6 single-spaced pages, including the prompts. If

needed, insert no more than 2 additional pages of supporting documentation for the

videorecordings at the end of the commentary (e.g., digital copies of indiscernible materials

or transcriptions of inaudible comments). These additional pages do not count toward the

commentary page limit noted above.

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1. Which lesson or lessons are shown in the video clip(s)? Identify the lesson(s) by lesson plan

number.

2. Promoting a Positive Learning Environment

Refer to scenes in the video clip(s) where you provided a positive learning environment.

a. How did you demonstrate mutual respect for, rapport with, and responsiveness to

students with varied needs and backgrounds, and challenge students to engage in

learning?

3. Engaging Students in Learning

Refer to examples from the video clip(s) in your responses to the prompts.

a. Explain how your instruction engaged students in developing understanding of

mathematical concepts.

b. Describe how your instruction linked students’ prior academic learning and personal,

cultural, and community assets with new learning.

4. Deepening Student Learning during Instruction

Refer to examples from the video clip(s) in your explanations.

a. Explain how you elicited and built on student responses to promote thinking and

develop understandings of mathematical concepts.

b. Explain how you used representations (manipulatives, models, tools, diagrams,

charts) to support students’ understanding and use of mathematical concepts.

5. Analyzing Teaching

Refer to examples from the video clip(s) in your responses to the prompts.

a. What changes would you make to your instruction—for the whole class and/or for

students who need greater support or challenge—to better support student learning of

the central focus (e.g., missed opportunities)?

Consider the variety of learners in your class who may require different

strategies/support (such as students with IEPs or 504 plans, English language

learners, struggling readers, underperforming students or those with gaps in

academic knowledge, and/or gifted students).

b. Why do you think these changes would improve student learning? Support your

explanation with evidence of student learning AND principles from theory and/or

research.

How Will the Evidence of My Teaching Practice Be

Assessed?

For Instruction Task 2, your evidence will be assessed using rubrics 6–10, which appear in

the following pages. When preparing your artifacts and commentaries, refer to the rubrics

frequently to guide your thinking, instruction, and writing.

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Instruction Rubrics

Rubric 6: Learning Environment

How does the candidate demonstrate a respectful learning environment that supports students’ engagement in

learning?

Level 1

The clip(s) reveal evidence of

disrespectful interactions

between teacher and students

or between students.

Candidate allows disruptive

behavior to interfere with

student learning.

Level 2

The candidate demonstrates

respect for students.

AND

Candidate provides a learning

environment that serves

primarily to control student

behavior, and minimally

supports the learning goals.

Level 3

The candidate demonstrates

rapport with and respect for

students.

AND

Candidate provides a positive,

low-risk learning

environment that reveals

mutual respect among

students.

Level 4

The candidate demonstrates

rapport with and respect for

students.

AND

Candidate provides a

challenging learning

environment that promotes

mutual respect among

students.

Level 5

The candidate demonstrates

rapport with and respect for

students.

AND

Candidate provides a

challenging learning

environment that provides

opportunities to express

varied perspectives and

promotes mutual respect

among students.

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Instruction Rubrics continued

Rubric 7: Engaging Students in Learning

How does the candidate actively engage students in developing understanding of mathematical concepts?

Level 1

Students are participating in

tasks that are vaguely or

superficially related to the

central focus.

There is little or no evidence

that the candidate links

students’ prior academic

learning or personal,

cultural, or community

assets with new learning.

Level 2

Students are participating in

learning tasks focusing

primarily on mathematical

skills OR procedures with

little attention to developing

understanding of

mathematical concepts.

Candidate makes vague or

superficial links between prior

academic learning and new

learning.

Level 3

Students are engaged in

learning tasks that address

understanding of

mathematical concepts.

Candidate links prior

academic learning to new

learning.

Level 4

Students are engaged in

learning tasks that develop

understanding of mathematical

concepts.

Candidate links prior academic

learning AND personal,

cultural, or community

assets to new learning.

Level 5

Students are engaged in

learning tasks that deepen

and extend their

understanding of mathematical

concepts.

Candidate prompts students

to link prior academic learning

AND personal, cultural, or

community assets to new

learning.

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Instruction Rubrics continued

Rubric 8: Deepening Student Learning

How does the candidate elicit responses to promote thinking and develop understanding of mathematical

concepts?

Level 1

Candidate does most of the

talking and students provide

few responses.

Candidate responses include

significant content

inaccuracies that will lead to

student misunderstandings.

Level 2

Candidate primarily asks

surface-level questions and

evaluates student responses as

correct or incorrect.

Level 3

Candidate elicits student

responses related to

mathematical reasoning or

problem solving to develop

understanding of a

mathematical concept.

Level 4

Candidate elicits and builds on

students’ mathematical

reasoning or problem solving

to explicitly portray, extend,

or clarify a mathematical

concept.

Level 5

Level 4 plus:

Candidate facilitates

interactions among

students to develop

understanding of a

mathematical concept.

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Instruction Rubrics continued

Rubric 9: Subject-Specific Pedagogy: Using Representations

How does the candidate use representations to develop students’ mathematical concepts?

Level 1

Candidate stays focused on

facts or procedures with little

or no attention to

mathematical concepts.

Materials used in the clips

include significant content

inaccuracies that will lead to

student misunderstandings.

Level 2

Candidate makes vague or

superficial use of

representations to help

students understand

mathematical concepts.

Level 3

Candidate uses

representations in ways that

help students understand

mathematical concepts.

Level 4

Candidate uses

representations in ways that

deepen student

understanding of

mathematical concepts.

Level 5

Level 4 plus:

Candidate facilitates

interactions among students

so they develop or apply

representations in ways that

deepen and extend their

understanding of

mathematical concepts.

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Instruction Rubrics continued

Rubric 10: Analyzing Teaching Effectiveness

How does the candidate use evidence to evaluate and change teaching practice to meet students’ varied

learning needs?

Level 1

Candidate suggests changes

unrelated to evidence of

student learning.

Level 2

Candidate proposes changes

to teacher practice that are

superficially related to student

learning needs (e.g., task

management, pacing,

improving directions).

Level 3

Candidate proposes changes

that address students’

collective learning needs

related to the central focus.

Candidate makes superficial

connections to research

and/or theory.

Level 4

Candidate proposes changes

that address individual and

collective learning needs

related to the central focus.

Candidate makes

connections to research

and/or theory.

Level 5

Level 4 plus:

Candidate justifies changes

using principles of research

and/or theory.

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Assessment Task 3: Assessing Student

Learning

What Do I Need to Think About?

In Assessment Task 3, you will analyze both student learning and student use of language.

Before you begin the analysis, you need to think about the following:

 How will you gather evidence and make sense of what students have learned?

 How will you provide meaningful feedback to your students?

 How will you use evidence of what students know and are able to do to plan next

steps in instruction?

 How will you identify evidence of and explain students’ use of language that

demonstrates the development of content understanding?

What Do I Need to Do?

 Select one assessment from your learning segment you will use to evaluate your

students’ developing knowledge and skills. It should be an assessment that is completed

by the whole class featured in the learning segment. (If you are teaching only a group

within the class for the learning segment, that group will be “the whole class.”) The

assessment should reflect the work of individuals, not groups, but may be individual

work from a group task. The assessment should provide opportunities for students to

demonstrate

 conceptual understanding

 procedural fluency

 mathematical reasoning or problem-solving skills

 Define and submit the evaluation criteria you will use to analyze student learning

related to the mathematical understandings described above.

 Collect and analyze student work from the selected assessment to identify

quantitative and qualitative patterns of learning within and across learners in the class.

You may submit text files with scanned student work OR, for oral assessments of

primary grade students (e.g., counting), a video or audio file. For each focus student, a

video or audio work sample must be no more than 5 minutes total running time. Select 3

student work samples that represent the patterns of learning (i.e., what individuals or

groups generally understood and what a number of students were still struggling to

understand) you identified in your assessment analysis. These students will be your

focus students for this task. At least one of the focus students must have specific

learning needs, for example, a student with an IEP (Individualized Education Program)

or 504 plan, an English language learner, a struggling reader, an underperforming

student or a student with gaps in academic knowledge, and/or a gifted student needing

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greater support or challenge. Note: California candidates must include one focus student

who is an English language learner.

 Document the feedback you gave to each of the 3 focus students on the work sample

itself, as an audio clip, or as a video clip. You must submit evidence of the actual

feedback provided to each focus student, and not a description of the feedback.

 If you submit a student work sample or feedback as a video or audio clip and comments

made by you or your focus student(s) cannot be clearly heard, attach a transcription of

the inaudible comments (no more than 2 additional pages) to the end of the

Assessment Commentary.

 If you submit a student work sample or feedback as a video or audio clip and additional

students are present, clearly identify which students are your focus students in prompt

1d of the Assessment Commentary (in no more than 2 sentences).

 Respond to the prompts listed in the Assessment Commentary section below after

analyzing student work from the selected assessment.

 Include and submit the selected assessment, including directions/prompts provided

to students. Attach the assessment (no more than 5 additional pages) to the end of the

Assessment Commentary.

 Provide evidence of students’ understanding and use of the targeted academic language

function and other language demands. You may choose evidence from the video clip(s)

submitted in Instruction Task 2, an additional video clip of one or more students using

language within the learning segment (no more than 5 minutes in length), AND/OR

student work samples submitted in Assessment Task 3.

See the Assessment Task 3: Artifacts and Commentary Specifications in the

Elementary Mathematics Evidence Chart for instructions on electronic submission of

evidence. This evidence chart identifies templates, supported file types, number of

files, response length, and other important evidence specifications. Your evidence

cannot contain hyperlinked content. Any web content you wish to include as part of

your evidence must be submitted as a document file, which must conform to the file

format and response length requirements.

What Do I Need to Write?

Assessment Commentary

In Assessment Task 3, you will write a commentary, responding to the prompts below. Your

commentary should be no more than 10 single-spaced pages, including the prompts.

Attach the assessment used to evaluate student performance (no more than 5 additional

pages) and, if necessary, a transcription of inaudible portions of a video or audio clip of

feedback or a student work sample (no more than 2 additional pages) to the end of the

Assessment Commentary. These additional pages do not count toward the commentary

page limit noted above.

California candidates—If you do not have any English language learners, select a student who is challenged by academic

English.

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1. Analyzing Student Learning

a. Identify the specific learning objectives measured by the assessment you chose for

analysis.

b. Provide a graphic (table or chart) or narrative that summarizes student learning for

your whole class. Be sure to summarize student learning for all evaluation criteria

submitted in Assessment Task 3, Part D.

c. Use evidence found in the 3 student work samples and the whole class summary

to analyze the patterns of learning for the whole class and differences for groups or

individual learners relative to

 conceptual understanding

 procedural fluency AND

 mathematical reasoning or problem-solving skills

Consider what students understand and do well, and where they continue to

struggle (e.g., common errors, confusions, need for greater challenge).

d. If a video or audio work sample occurs in a group context (e.g., discussion), provide

the name of the clip and clearly describe how the scorer can identify the focus

student(s) (e.g., position, physical description) whose work is portrayed.

2. Feedback to Guide Further Learning

Refer to specific evidence of submitted feedback to support your explanations.

a. Identify the format in which you submitted your evidence of feedback for the

3 focus students. Choose one of the following:

 Written directly on work samples or in separate documents that were

provided to the focus students

 In audio files

 In video clip(s) from Instruction Task 2 (provide a time-stamp reference) or in

separate video clips

If a video or audio clip of feedback occurs in a group context (e.g., discussion),

clearly describe how the scorer can identify the focus student (e.g., position,

physical description) who is being given feedback.

b. Explain how feedback provided to the 3 focus students addresses their individual

strengths and needs relative to the learning objectives measured.

c. Describe how you will support each focus student to understand and use this

feedback to further their learning related to learning objectives, either within the

learning segment or at a later time.

3. Evidence of Language Understanding and Use

When responding to the prompt below, use concrete examples from the video clip(s)

and/or student work samples as evidence. Evidence from the clip(s) may focus on

one or more students.

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You may provide evidence of students’ language use from ONE, TWO, OR

ALL THREE of the following sources:

1. Use video clip(s) from Instruction Task 2 and provide time-stamp

references for evidence of language use.

2. Submit an additional video file named “Language Use” of no more than

5 minutes in length and cite language use (this can be footage of one or

more students’ language use). Submit the clip in Assessment Task 3,

Part B.

3. Use the student work samples analyzed in Assessment Task 3 and cite

language use.

a. Explain and provide concrete examples for the extent to which your students were

able to use or struggled to use the

 selected language function,

 vocabulary and/or symbols, AND

 discourse or syntax

to develop content understandings.

4. Using Assessment to Inform Instruction

a. Based on your analysis of student learning presented in prompts 1b–c, describe next

steps for instruction:

 For the whole class

 For the 3 focus students and other individuals/groups with specific needs

Consider the variety of learners in your class who may require different

strategies/support (e.g., students with IEPs or 504 plans, English language

learners, struggling readers, underperforming students or those with gaps in

academic knowledge, and/or gifted students needing greater support or

challenge).

b. Explain how these next steps follow from your analysis of student learning. Support

your explanation with principles from research and/or theory.

How Will the Evidence of My Teaching Practice Be

Assessed?

For Assessment Task 3, your evidence will be assessed using rubrics 11–15, which appear

in the following pages. When preparing your artifacts and commentaries, refer to the rubrics

frequently to guide your thinking, planning, instruction, assessment, and writing.

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Assessment Rubrics

Rubric 11: Analysis of Student Learning

How does the candidate analyze evidence of student learning of conceptual understanding, procedural fluency,

and mathematical reasoning/problem-solving skills?

Level 1

The analysis is superficial or

not supported by either student

work samples or the summary

of student learning.

The evaluation criteria, learning

objectives, and/or analysis are

not aligned with each other.

Level 2

The analysis focuses on what

students did right OR wrong.

Level 3

The analysis focuses on what

students did right AND wrong.

AND

Analysis includes some

differences in whole class

learning.

Level 4

Analysis uses specific

examples from work samples to

demonstrate patterns of

learning consistent with the

summary.

AND

Patterns of learning are

described for whole class.

Level 5

Analysis uses specific

evidence from work

samples to demonstrate

the connections

between quantitative

and qualitative patterns

of learning for

individuals or groups.

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Assessment Rubrics continued

Rubric 12: Providing Feedback to Guide Learning

What type of feedback does the candidate provide to focus students?

Level 1

Feedback is unrelated to the

learning objectives OR is

developmentally

inappropriate.

Feedback contains

significant content

inaccuracies.

No feedback is provided to

one or more focus students.

Level 2

Feedback is general and

addresses needs AND/OR

strengths related to the

learning objectives.

Level 3

Feedback is specific and

addresses either needs OR

strengths related to the

learning objectives.

Level 4

Feedback is specific and

addresses both strengths

AND needs related to the

learning objectives.

Level 5

Level 4 plus:

Feedback for one or more

focus students

• provides a strategy to

address an individual

learning need OR

• makes connections to

prior learning or

experience to improve

learning.

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Assessment Rubrics continued

Rubric 13: Student Use of Feedback

How does the candidate support focus students to understand and use the feedback to guide their further

learning?

Level 1

Opportunities for using

feedback are not described.

Candidate provides limited or

no feedback to inform

student learning.

Level 2

Candidate provides vague

description of how focus

students will understand or

use feedback.

Level 3

Candidate describes how

focus students will understand

or use feedback related to

learning objectives.

Level 4

Candidate describes how s/he

will support focus students to

understand and use

feedback on their strengths

OR weaknesses related to

learning objectives.

Level 5

Candidate describes how s/he

will support focus students to

understand and use

feedback on their strengths

AND weaknesses related to

the learning objectives.

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Assessment Rubrics continued

Rubric 14: Analyzing Students’ Language Use and Mathematics Learning

How does the candidate analyze students' use of language to develop content understanding?

Level 1

Candidate identifies student

language use that is

superficially related or

unrelated to the language

demands (vocabulary and/or

symbols, function,

and

additional demands).

Candidate’s description or

explanation of language use

is not consistent with the

evidence submitted.

Level 2

Candidate describes how

students use only one

language demand

(vocabulary and/or symbols,

function, discourse, syntax).

Level 3

Candidate explains and

provides evidence of

students’ use of

• the language function

AND

• one or more additional

language demands

(vocabulary and/or

symbols, discourse,

syntax).

Level 4

Candidate explains and

provides evidence of students’

use of

• the language function,

• vocabulary and/or

symbols, AND

• additional language

demand(s) (discourse,

syntax)

in ways that develop content

understandings.

Level 5

Level 4 plus:

Candidate explains and

provides evidence of

language use and content

learning for students with

varied needs.

The selected language function is the verb identified in the Planning Commentary Prompt 4a (categorize, describe, interpret, etc.).

These are the additional language demands identified in the Planning Commentary Prompt 4c (vocabulary and/or symbols, plus either syntax or discourse).

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Assessment Rubrics continued

Rubric 15: Using Assessment to Inform Instruction

How does the candidate use the analysis of what students know and are able to do to plan next steps in

instruction?

Level 1

Next steps do not follow from

the analysis.

Next steps are not relevant to

the learning objectives

assessed.

Next steps are not described

in sufficient detail to

understand them.

Level 2

Next steps primarily focus on

changes to teaching practice

that are superficially related

to student learning needs,

for example, repeating

instruction, pacing, or

classroom management

issues.

Level 3

Next steps propose general

support that improves

student learning related to

assessed learning

objectives.

Next steps are loosely

connected with research

and/or theory.

Level 4

Next steps provide targeted

support to individuals or

groups to improve their

learning relative to

• conceptual understanding,

• procedural fluency,

AND/OR

• mathematical reasoning

and/or problem-solving

skills.

Next steps are connected

with research and/or theory.

Level 5

Next steps provide targeted

support to individuals AND

groups to improve their

learning relative to

• conceptual understanding,

• procedural fluency,

AND/OR

• mathematical reasoning

and/or problem-solving

skills.

Next steps are justified with

principles from research

and/or theory.

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Professional Responsibilities

Refer to the following table for an overview of your professional responsibilities in

developing evidence for edTPA. If you are submitting artifacts and commentaries for official

scoring, refer to www.edTPA.com

, for complete and current information before beginning

your work. Included here are important information and policies such as submission

requirements and deadlines, registration agreements, attestations, permissions, and

confidentiality. Whether or not you are submitting for official scoring, you should fulfill the

professional responsibilities described below.

Responsibility Description

Protect

confidentiality

To protect confidentiality, please remove your name and use pseudonyms or general

references (e.g., “the district”) for your state, school, district, and cooperating teacher. Mask or

remove all names on any typed or written material (e.g., commentaries, lesson plans, student

work samples) that could identify individuals or institutions. During videorecording, use

students’ first names only.

To ensure confidentiality of your students and yourself, do not share your video on any publicly

accessible platforms or websites (YouTube, Facebook, etc.).

Acquire

permissions

Before you record your classroom instruction, ensure that you have the appropriate permission

from the parents/guardians of your students and from adults who appear in the videorecording.

Your program will provide you with procedures and necessary forms to obtain these

permissions, according to agreements with the school or district in which you are student

teaching or completing your internship.

If your program does not provide the necessary forms, you may refer to the sample forms

found on www.edTPA.com

The release forms are not to be submitted with your materials, but you should follow your

campus policy for retaining them.

Cite sources

Provide citations for the source of all materials that you did not create (e.g., published texts,

websites, and material from other educators). List all citations by lesson number at the end of

the Planning Commentary.

Align instruction

with state

standards

As part of the assessment, you will document the alignment of your lesson plans with state-

adopted academic content standards that are the target of student learning. Refer to the

education agency website for your state to obtain copies of relevant standards for this

assessment.

Follow the

guidelines for

candidate

support at

www.edTPA.com

Follow the guidelines for candidate support found at www.edTPA.com as you develop your

evidence for edTPA. Although you may seek and receive appropriate support from your

university supervisors, cooperating/master teachers, university instructors, or peers during this

process, the ultimate responsibility for completing this assessment lies with you. Therefore,

when you submit your completed work, you must be able to confirm your adherence

with certain statements, such as the following:

 I have primary responsibility for teaching the students/class during the learning segment

profiled in this assessment.

 I have not previously taught this learning segment to the students/class.

 The video clips submitted are unedited (continuous) and show me teaching the

students/class profiled in the evidence submitted.

 The student work included in the documentation is that of my students, completed during

the learning segment documented in this assessment.

 I am author of the commentaries and other written responses to prompts in this

assessment.

 Appropriate citations have been made for all materials in the assessment whose sources

are from published text, the Internet, or other educators.

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Elementary Mathematics Context for

Learning Information

Use the Context for Learning Information to supply information about your school/classroom

context.

About the School Where You Are Teaching

1. In what type of school do you teach? (Type an "X" next to the appropriate description.)

Urban: _____

Suburban: _____

Rural: _____

2. What grade levels are at your school site (e.g., K–6)?

3. List any special features of your school or classroom setting (e.g., charter, co-teaching,

themed magnet, classroom aide, bilingual, team taught with a special education teacher) that

will affect your teaching in this learning segment.

4. Describe any district, school, or cooperating teacher requirements or expectations that might

affect your planning or delivery of instruction, such as required curricula, pacing plan, use of

specific instructional strategies, or standardized tests.

About the Class Featured in this Learning Segment

1. How much time is devoted each day to mathematics instruction in your classroom?

2. Is there any ability grouping or tracking in mathematics? If so, please describe how it affects

your class.

3. Identify any textbook or instructional program you primarily use for mathematics instruction. If

a textbook, please provide the title, publisher, and date of publication.

4. List other resources (e.g., electronic whiteboard, manipulatives, online resources) you use

for mathematics instruction in this class.

edTPA Elementary Mathematics Assessment Handbook

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About the Students in the Class Featured in this Learning Segment

1. Grade-level(s): ____________________________________

2. Number of

 students in the class: _____

 males: _____ females: _____

3. Complete the charts below to summarize required or needed supports, accommodations, or

modifications for your students that will affect your instruction in this learning segment. As

needed, consult with your cooperating teacher to complete the charts. Some rows have been

completed in italics as examples. Use as many rows as you need.

Consider the variety of learners in your class who may require different

strategies/supports or accommodations/modifications to instruction or

assessment. For example, students



With Individualized Education Programs (IEPs) or 504 plans



With specific language needs



Needing greater challenge or support



Who struggle with reading



Who are underperforming students or have gaps in academic knowledge

For Assessment Task 3, you will choose work samples from 3 focus students. At

least one of these students must have a specified learning need. Note: California

candidates must include one focus student who is an English language learner.

Students with IEPs/504 Plans

IEPs/504 Plans:

Classifications/Needs

Number of

Students

Supports, Accommodations,

Modifications, Pertinent IEP Goals

Example: Visual processing

Close monitoring, graph paper for 3 digit

numbers

California candidates—If you do not have any English language learners, select a student who is challenged by academic

English.

edTPA Elementary Mathematics Assessment Handbook

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Students with Specific Language Needs

Language Needs

Number of

Students

Supports, Accommodations,

Modifications

Example: English language

learners with only a few

words of English

Pre-teach key words and phrases

through examples and graphic

organizers (e.g., word cluster,

manipulatives, visuals)

Have students use pre-taught key words

and graphic organizers to

complete sentence starters

Example: Students who

speak a variety of English

other than that used in

textbooks

Make connections between the language

students bring and the language used in

the textbook

Students with Other Learning Needs

Other Learning Needs

Number of

Students

Supports, Accommodations,

Modifications

Example: Struggling readers

Provide oral explanations for directions

and simplified text for word problems

edTPA Elementary Mathematics Assessment Handbook

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Elementary Mathematics Evidence Chart

Your evidence must be submitted to the electronic portfolio management system used by your teacher preparation program. Your

submission must conform to the artifact and commentary specifications for each task. This section provides instructions for all

evidence types as well as a description of supported file types for evidence submission, number of files, response lengths, and

other information regarding format specifications. Note that your evidence cannot contain hyperlinked content. Any web content

you wish to include as part of your evidence must be submitted as a document file, which must conform to the file format and

response length requirements.

Planning Task 1: Artifacts and Commentary Specifications

What to

Submit

Supported File

Types

Number of Files

Response

Length

Additional Information

Min

Max

Part A: Context

for Learning

Information

(template

provided)

.doc; .docx; .odt; .pdf

No more than 4

pages, including

prompts



Use Arial 11-point type.

 Single space with 1" margins on all sides.

Part B: Lesson

Plans for

Learning

Segment

.doc; .docx; .odt; .pdf

1 1

No more than 4

pages per lesson

 Submit 3–5 lesson plans in 1 file.

 Within the file, label each lesson plan (Lesson 1, Lesson 2, etc.).

 All rationale or explanation for plans should be written in the Planning

Commentary and removed from lesson plans.

Part C:

Instructional

Materials

.doc; .docx; .odt; .pdf

No more than 5

pages of KEY

instructional materials

per lesson plan



Submit all materials in 1 file.

 Within the file, label materials by corresponding lesson (Lesson 1

Instructional Materials, Lesson 2 Instructional Materials, etc.).

 Order materials as they are used in the learning segment.

Part D:

Assessments

.doc; .docx; .odt; .pdf

N/A



Submit assessments in 1 file.

 Within the file, label assessments by corresponding lesson

(Lesson 1 Assessments, Lesson 2 Assessments, etc.).

 Order assessments as they are used in the learning segment.

Part E: Planning

Commentary

(template

provided)

.doc; .docx; .odt; .pdf

No more than 9

pages of

commentary,

including prompts



Use Arial 11-point type.

 Single space with 1" margins on all sides.

 Respond to prompts before teaching the learning segment.

edTPA Elementary Mathematics Assessment Handbook

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Instruction Task 2: Artifacts and Commentary Specifications

What to

Submit

Supported File

Types

Number of Files

Response

Length

Additional Information

Min

Max

Part A: Video

Clips

flv, asf, qt, mov, mpg,

mpeg, avi, wmv, mp4,

m4v

No more than

15 minutes total

running time



Before you record your video, obtain permission from the

parents/guardians of your students and from adults who appear

on the video.

 Refer to Instruction Task 2, What Do I Need to Do? for video clip

content and requirements.

 When naming each clip file, include the number of the lesson

shown in the video clip.

Part B:

Instruction

Commentary

(template

provided)

.doc; .docx; .odt; .pdf

1 1

No more than

pages of

commentary,

including prompts

If needed, no more

than 2 additional

pages of supporting

documentation

 Use Arial 11-point type.

 Single space with 1" margins on all sides.

 Respond to prompts after teaching the learning segment.

IMPORTANT:

 Insert documentation at the end of the commentary file if

 you or the students are using graphics, texts, or images that

are not clearly visible in the video

 you chose to submit a transcript for occasionally inaudible

portions of the video

 If submitting documentation, include the video clip number, lesson

number, and explanatory text (e.g., “Clip 1, lesson 2, text from a

whiteboard that is not visible in the video,” “Clip 2, lesson 4,

transcription of a student response that is inaudible”).

edTPA Elementary Mathematics Assessment Handbook

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Assessment Task 3: Artifacts and Commentary Specifications

What to

Submit

Supported File

Types

Number of Files

Response

Length

Additional Information

Min

Max

Part A: Student

Work Samples

For written work

samples: .doc; .docx;

.odt; .pdf

For audio work

samples: flv, asf, wmv,

qt, mov, mpg, avi, mp3,

wav, mp4, wma

For video work

samples: flv, asf, qt,

mov, mpg, mpeg, avi,

wmv, mp4, m4v

No more than

5 minutes per focus

student for video or

audio student work

samples



For written work samples, use correction fluid, tape, or a felt-tip

marker to mask or remove students’ names, your name, and

the name of the school before copying/scanning any work

samples. If your students’ writing is illegible, write a transcription

directly on the work sample.

 On each work sample, indicate the student number (Student 1

Work Sample, Student 2 Work Sample, or Student 3 Work

Sample). If more than one focus student appears in a video or

audio work sample, upload the same work sample separately for

each focus student who is seen/heard and label appropriately.

Describe how to recognize each of the focus students in the clip

and provide the label associated with the clip in prompt 1d of the

Assessment Commentary

 When naming each work sample file, include the student number.

 If you submit a work sample as a video or audio clip and there are

audio portions that cannot be heard clearly, attach a transcription

of the inaudible portions to the end of the Assessment

Commentary.

(Continued on next page)

edTPA Elementary Mathematics Assessment Handbook

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Assessment Task 3: Artifacts and Commentary Specifications (continued)

What to

Submit

Supported File

Types

Number of Files

Response

Length

Additional Information

Min

Max

Part B: Evidence

of Feedback

And, if included,

video evidence of

academic

language use

For written feedback

not written on the work

samples: .doc; .docx;

.odt; .pdf

For audio feedback: flv,

asf, wmv, qt, mov, mpg,

avi, mp3, wav, mp4,

wma

For video clips

(feedback and/or

language use): flv, asf,

qt, mov, mpg, mpeg, avi,

wmv, mp4, m4v

No page limit for

written feedback

No more than 3

minutes per focus

student for video or

audio feedback

No more than 5

minutes for video

evidence of student

language use



Document the location of your evidence of feedback in the

Assessment Commentary.

 If feedback is not included as part of the student work samples or

recorded on the video clip(s) from Instruction Task 2, submit only 1

file for each focus student—a document, video file, OR audio file—

and label the file with the corresponding student number (Student

1 Feedback, Student 2 Feedback, or Student 3 Feedback).

 When naming each feedback file, include the student number.

 If you submit feedback as a video or audio clip and your comments

cannot be clearly heard, attach a transcription of your comments to

the end of the Assessment Commentary.

 For Academic Language—If you choose to submit a video clip of

student language use, it should be no more than 5 minutes. You

may identify a portion of a clip provided for Instruction Task 2 or

submit an entirely new clip.

(Continued on next page)

edTPA Elementary Mathematics Assessment Handbook

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Assessment Task 3: Artifacts and Commentary Specifications (continued)

What to

Submit

Supported File

Types

Number of Files

Response

Length

Additional Information

Min

Max

Part C:

Assessment

Commentary

(template

provided)

.doc; .docx; .odt; .pdf

No more than 10

pages of

commentary,

including prompts

Plus

 no more than 5

additional pages

for the chosen

assessment,

 if necessary, no

more than 2

additional total

pages of

transcription of

video/audio

evidence for a

work sample and

feedback, and/or

video evidence of

language use.



Use Arial 11-point type.

 Single space with 1" margins on all sides.

IMPORTANT: Insert a copy of the chosen assessment, including

directions/prompts provided to students.

Part D: Evaluation

Criteria

.doc; .docx; .odt; .pdf

N/A

edTPA Elementary Mathematics Assessment Handbook

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Elementary Mathematics Glossary

Source citations for glossary entries are provided as footnotes in this section.

academic language: Oral and written language used for academic purposes. Academic

language is the means by which students develop and express content understandings.

Academic language represents the language of the discipline that students need to learn

and use to participate and engage in the content area in meaningful ways. There are

language demands that teachers need to consider as they plan to support student learning

of content. These language demands include language functions, vocabulary and/or

symbols, discourse, and syntax.

 language demands:

Specific ways that academic language (vocabulary and/or

symbols, functions, discourse, syntax) is used by students to participate in learning

tasks through reading, writing, listening, and/or speaking to demonstrate their

disciplinary understanding.

 language functions: The content and language focus of the learning task,

represented by the active verbs within the learning outcomes. Common language

functions in mathematics include describing mathematical phenomena, predicting

from models and data, comparing based on common attributes, summarizing

mathematical information, recording multiple ways to solve problems, justifying

conclusions, evaluating data and mathematical representations, classifying based

on attributes, explaining how or why certain strategies work, drawing conclusions

based on data, representing mathematical information, and so on. Some specific

mathematics verbs are non-examples of language functions because they focus on a

mathematical action, not a language-based action. Examples of mathematical

functions that ARE NOT language functions include solving problems, simplifying

the expressions, calculating the answers, and estimating the answers.

 vocabulary: Includes words and phrases that are used within disciplines including:

(1) words and phrases with subject-specific meanings that differ from meanings used

in everyday life (e.g., table); (2) general academic vocabulary used across disciplines

(e.g., compare, analyze, evaluate); and (3) subject-specific words defined for use in

the discipline.

 discourse: Discourse includes the structures of written and oral language, as well as

how students talk, write, and participate in knowledge construction in ways that are

appropriate both to their development and to the discipline. Discipline-specific

discourse has distinctive features or ways of structuring oral or written language (text

O'Hara, S., Pritchard, R., & Zwiers, J. (2012). Identifying academic language demands in support of the common core

standards. ASCD Express, 7(17). Retrieved from http://www.ascd.org/ascd-express/vol7/717-ohara.aspx

Quinn, H., Lee, O., & Valdés, G. (2012). Language demands and opportunities in relation to next generation science

standards for English language learners: What teachers need to know. Retrieved from

http://ell.stanford.edu/sites/default/files/pdf/academic-papers/03-

Quinn%20Lee%20Valdes%20Language%20and%20Opportunities%20in%20Science%20FINAL.pdf

edTPA Elementary Mathematics Assessment Handbook

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structures) that provide useful ways for the content to be communicated.

mathematics, language structures include symbolic representations such as

numbers, equations, and proofs (which can be translated into words), tables and

graphs (which are shorthand language for summarizing complex sets of data), and

narrative (e.g., explanations of problem solutions). If the function is to compare, then

appropriate language forms could include Venn diagrams or pattern sentences such

as “The _____ is longer/larger/heavier than the ______.” If the function is to explain,

then students might use sentence starters like “First, I…”, “Then I…” to structure the

explanation, and use “Finally, I…” to signal the conclusion.

 syntax: The set of conventions for organizing symbols, words, and phrases together

into structures (e.g., sentences, graphs, tables).

 language supports: The scaffolds, representations, and pedagogical strategies

teachers provide to help learners understand, use, and practice the concepts and

language they need to learn within disciplines (Santos, Darling-Hammond, Cheuk,

2012).

The language supports planned within the lessons in edTPA should directly

support learners to understand and use identified language demands (vocabulary

and/or symbols, language function, and discourse or syntax) to deepen content

understandings.

aligned: Consistently addressing the same/similar learning outcomes for students.

artifacts: Authentic work completed by you and your students, including lesson plans,

copies of instructional and assessment materials, video clips of your teaching, and student

work samples. Artifacts are submitted as part of your edTPA evidence.

assessment (formal and informal): “[R]efer[s] to all those activities undertaken by

teachers and by their students . . . that provide information to be used as feedback to modify

the teaching and learning activities.”

Assessments provide evidence of students’ prior

knowledge, thinking, or learning in order to evaluate what students understand and how they

are thinking. Informal assessments may include, for example, student questions and

responses during instruction and teacher observations of students as they work or perform.

Formal assessments may include, for example, quizzes, homework assignments, journals,

projects, and performance tasks.

assets (knowledge of students):

 personal: Refers to specific background information that students bring to the

learning environment. Students may bring interests, knowledge, mathematical

dispositions, everyday experiences, family backgrounds, and so on, which a teacher

can draw upon to support learning.

Quinn, H., Lee, O., & Valdés, G. (2012). Language demands and opportunities in relation to next generation science

standards for English Language Learners: What teachers need to know. Retrieved from

http://ell.stanford.edu/sites/default/files/pdf/academic-papers/03-

Quinn%20Lee%20Valdes%20Language%20and%20Opportunities%20in%20Science%20FINAL.pdf

Zwiers, J. (2008). Building academic language: Essential practices for content classrooms. San Francisco, CA: Jossey-Bass.

Santos, M., Darling-Hammond, L., & Cheuk, T. (2012). Teacher development to support

English language learners in the context of common core state standards. Stanford University Understanding Language.

Available at

http://ell.stanford.edu/sites/default/files/pdf/academic-papers/10-

Santos%20LDH%20Teacher%20Development%20FINAL.pdf

Black, P., & Wiliam, D. (1998). Inside the black box: Raising standards through classroom assessment. Phi Delta Kappan,

80(2), 139–148.

edTPA Elementary Mathematics Assessment Handbook

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 cultural: Refers to the cultural backgrounds and practices that students bring to the

learning environment, such as traditions, languages and dialects, worldviews,

literature, art, and so on, that a teacher can draw upon to support learning.

 community: Refers to common backgrounds and experiences that students bring

from the community where they live, such as resources, local landmarks, community

events and practices, and so on, that a teacher can draw upon to support learning.

central focus: A description of the important understandings and core concepts that you

want students to develop within the learning segment. The central focus should go beyond a

list of facts and skills, align with content standards and learning objectives, and address the

subject-specific components in the learning segment. For example, the subject-specific

components for elementary mathematics are conceptual understanding, procedural fluency,

AND mathematical reasoning or problem-solving skills. A central focus for the elementary

mathematics learning segment might be equivalent fractions or equivalencies. The learning

segment would focus on conceptual understanding and the associated

computational/procedural understandings AND reasoning or problem-solving skills.

commentary: Submitted as part of each task and, along with artifacts, make up your

evidence. The commentaries should be written to explain the rationale behind your teaching

decisions and to analyze and reflect on what you have learned about your teaching practice

and your students’ learning.

conceptual understanding: “Students demonstrate conceptual understanding in

mathematics . . . when they recognize, label, and generate examples of concepts; use and

interrelate models, diagrams, manipulatives, and varied representations of concepts; identify

and apply principles; know and apply facts and definitions; compare, contrast, and integrate

related concepts and principles; recognize, interpret, and apply the signs, symbols, and

terms used to represent concepts.”

engaging students in learning: Using instructional and motivational strategies that

promote students’ active involvement in learning tasks that increase their knowledge, skills,

and abilities related to specific learning objectives. Engagement in learning contrasts with

student participation in learning tasks that are not well designed and/or implemented and do

not increase student learning.

evaluation criteria: Performance indicators or dimensions that are used to assess evidence

of student learning. They indicate the qualities by which levels of performance can be

differentiated and that anchor judgments about the learner’s degree of success on an

assessment. Evaluation criteria can be represented in various ways, such as a rubric, a

point system for different levels of performance, or rules for awarding full versus partial

credit. Evaluation criteria may examine correctness/accuracy, cognitive complexity,

sophistication or elaboration of responses, or quality of explanations.

evidence: Consists of artifacts that document how you planned and implemented

instruction AND commentaries that explain your plans and what is seen in the

videorecording(s) or examine what you learned about your teaching practice and your

students’ learning. Evidence should demonstrate your ability to design lesson plans with

instructional supports that deepen student learning, use knowledge of your students to

National Assessment of Educational Progress (NAEP). (2003). Conceptual understanding. In What Does the NAEP

Mathematics Assessment Measure? Retrieved from: http://nces.ed.gov/nationsreportcard/mathematics/abilities.asp

edTPA Elementary Mathematics Assessment Handbook

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inform instruction, foster a positive learning environment that promotes student learning,

monitor and assess student progress toward learning objectives, and analyze your teaching

effectiveness. Your evidence must be submitted electronically using the electronic portfolio

management system used by your teacher preparation program.

learning environment: The designed physical and emotional context, established and

maintained throughout the learning segment to support a positive and productive learning

experience for students.

learning objectives: Student learning outcomes to be achieved by the end of the lesson or

learning segment.

learning segment: A set of 3–5 lessons that build one upon another toward a central focus,

with a clearly defined beginning and end.

learning task: Includes activities, discussions, or other modes of participation that engage

students to develop, practice, and apply skills and knowledge related to a specific learning

goal. Learning tasks may be scaffolded to connect prior knowledge to new knowledge and

often include formative assessment. A sample mathematical learning task for fourth graders

working with multi-digit numbers could be: Collect the population from 4 neighboring states

to compare with our own state. Identify the state with the highest and lowest populations and

make a table showing the states’ populations in order from highest to lowest populations.

Compare the populations of the states by writing statements using <, =, and >.

mathematical reasoning: “[T]he capacity to think logically about the relationships among

concepts and situations. Such reasoning is correct and valid, stems from careful

consideration of alternatives, and includes knowledge of how to justify the conclusions. One

uses it to navigate through the many facts, procedures, concepts, and solution methods and

to see that they all fit together in some way, that they make sense.”

mathematical understandings: Mathematical competencies (conceptual understanding

and procedural fluency) develop through instruction of mathematical topics. Mathematical

reasoning provides opportunities for students to develop and express insights about the

mathematical competencies that they are developing. Problem solving allows students to

draw on the competencies that they are developing to engage in a task for which the

solution is not known.

patterns of learning: Includes both quantitative and qualitative patterns (or consistencies)

for different groups of students or individuals. Quantitative patterns indicate in a numerical

way the information understood from the assessment (e.g., 10 out of 15 students or 20% of

the students). Qualitative patterns include descriptions of understandings,

misunderstandings, and/or partial understandings that could explain the quantitative

patterns (e.g., “given that most students were able to . . . it seems that they understand…”).

planned supports: Instructional strategies, learning tasks and materials, and other

resources deliberately designed to facilitate student learning of the central focus.

prior academic learning and prerequisite skills: Includes students’ content knowledge

and skills as well as academic experiences developed prior to the learning segment.

National Research Council. (2001). Adaptive reasoning. In Adding it up: Helping children learn mathematics (p. 151).

Washington, DC: National Academy Press.

edTPA Elementary Mathematics Assessment Handbook

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problem-solving skills: Skills to “engag[e] in a task for which the solution method is not

known in advance.”

rapport: A close and harmonious relationship in which the people or groups understand

each other’s feelings or ideas and communicate well with each other.

representations: Manipulatives, models, tools, charts, and/or graphics that are used to

deepen students’ understanding of mathematics knowledge.

respect: A positive feeling of esteem or deference for a person and specific actions and

conduct representative of that esteem. Respect can be a specific feeling of regard for the

actual qualities of the one respected. It can also be conduct in accord with a specific ethic of

respect. Rude conduct is usually considered to indicate a lack of respect, disrespect,

whereas actions that honor somebody or something indicate respect. Note that respectful

actions and conduct are culturally defined and may be context dependent.

rubrics: Subject-specific evaluation criteria used to score your performance on edTPA.

These rubrics are included in the handbook, following the directions for each task. The

descriptors in the five-level rubrics address a wide range of performance, beginning with the

knowledge and skills of a novice not ready to teach (Level 1) and extending to the advanced

practices of a highly accomplished beginner (Level 5).

variety of learners: Students in your class who may require different strategies or support.

These students include but are not limited to students with IEPs or 504 plans, English

language learners, struggling readers, underperforming students or those with gaps in

academic knowledge, and/or gifted students.

National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics (p. 52).

Reston, VA: NCTM.

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